Problem: What is the measure, in degrees, of the acute angle formed by the minute hand and the hour hand on a standard clock when it indicates $9$:$40$?
The hour hand is $40/60=2/3$ of the way from the 9 to the 10 on the clock, which the minute hand is on the 8. Between any two numbers on the clock there are $360/12=30$ degrees. Thus, the angle between the two hands is $30+30(2/3)=\boxed{50}$ degrees.